Thursday, October 3, 2019 1:00 pm
-
1:00 pm
EDT (GMT -04:00)
Title: Type II Matrices
| Speaker: | Ada Chan |
| Affiliation: | York University |
| Room: | MC 5479 |
Abstract:
In 1867, Sylvester defined an {\sl inverse orthogonal matrix} as an $n\times n$ complex matrix $W$ satisfying
\begin{equation*}
\sum_{k=1}^n \frac{W_{i,k}}{W_{j,k}} = \delta_{i,j} n,
\qquad \forall i,j.
\end{equation*}
Interests
in
these
matrices
resumed
in
the
1990's,
after
Jones'
construction
of
knot
invariants
using
spin
models.
The
term
{\sl
type
II}
was
coined
after
the
second
Reidemeister
move.
Interesting
examples
of
type
II
matrices
include
Hadamard
matrices,
character
table
of
finite
abelian
groups
and
spin
models.
In
this
talk,
we
introduce
type
II
matrices
and
describe
Nomura's
construction
of
a
formally
dual
pair
of
association
schemes
from
each
type
II
matrix.